A typical example of the filter circuit is illustrated in FIG. 1 and largely comprises two filter units 1 and 2 which have input nodes 3 and 4, output nodes 5 and 6 and control nodes 7 and 8, respectively. Both of the filter units 1 and 2 are of the voltage control type and, accordingly, responsive to the voltage levels at the respective control nodes for changing the cut-off frequencies. For this purpose, the filter units 1 and 2 are associated with a controller 9 which varies a control signal in voltage level on the basis of the adjustment of a variable resistor 10 coupled between the controller and a ground terminal. In detail, the circuit arrangement of the prior-art filter circuit is illustrated in FIG. 2 and implemented by a combination of n-p-n type bipolar transistors, p-n-p type bipolar transistors, capacitors and resistors. As shown in FIG. 2 of the drawings, the input node 3 is coupled to the base node of an n-p-n type bipolar transistor 11, and the output node 5 is coupled to the base node of an n-p-n type bipolar transistor 12. Two p-n-p type bipolar transistors 13 and 14 are coupled in parallel between a positive voltage source Vcc and the n-p-n type bipolar transistors 11 and 12, and the base nodes of the p-n-p type bipolar transistors 13 and 14 are commonly coupled to the collector node of the p-n-p type bipolar transistor 13. A series combination of an n-p-n type bipolar transistor 15 and a resistor 16 is coupled between the emitter nodes of the n-p-n type bipolar transistors 11 and 12 and the ground terminal. A series combination of an n-p-n type bipolar transistor 17 and a resistor 18 is coupled between the positive voltage source Vcc and the ground terminal, and the output node 5 is provided between the n-p-n type bipolar transistor 17 and the resistor 18. A capacitor 19 is coupled at one electrode thereof to the ground terminal, and the other electrode of the capacitor 19 is shared by the collector node of the p-n-p type bipolar transistor 14 and the base node of the n-p-n type bipolar transistor 17. The filter unit 1 thus arranged is similar in circuit arrangement to the filter unit 2, and, for this reason, component elements of the filter unit 2 corresponding to the component elements 11 to 19 are designated by reference numerals 21 to 29, respectively. The controller 9 is implemented by a series combination of a resistor 31 and the variable resistor 10 coupled between the positive voltage source Vcc and the ground terminal, and an output node 32 of the controller 9 is provided between the resistor 31 and the variable resistor 32 and coupled to the base electrodes of the n-p-n type bipolar transistors 15 and 25 for the sake of the variation of the cut-off frequencies.
Description is made for the adjustment of the cut-off frequencies. The cut-off frequency f.sub.L(1) of the filter unit 4 is calculated as follows: EQU f.sub.L(1) =g.sub.m /(2.times..pi..times.C.sub.19) (Eq. 1)
where C.sub.19 is the capacitance of the capacitor 19 and the mutual conductance g.sub.m is given by Equation 2. EQU g.sub.m =(q.times.I.sub.0)/(2.times.k.times.T)=1/r.sub.e (Eq. 2)
where q is the elementary charge of about 1.62.times.10.sup.-19 (C), k is the Boltzmann constant of about 1.38.times.10.sup.-23 (W.times.S/.degree.k), T is a temperature in Kelvin scale, and I.sub.0 is given by Equation 3. EQU I.sub.0 =[{R10/(R31+R10)}.times.Vcc-V.sub.BE(Q15) ].times.(1/R16) (Eq. 3)
where R10, R31 and R16 are respective resistances of the resistors 10, 31 and 16, Vcc is the difference in voltage level between the positive voltage source Vcc and the ground terminal, and V.sub.BE(Q15) is the emitter-base voltage of the n-p-n type bipolar transistor 15. As understood from the above equations, the filter unit 1 is varied in cut-off frequency by changing the mutual conductance g.sub.m which in turn is adjusted by manually changing the resistance R10 of the variable resistor 10.
The filter unit 2 is adjusted to have a different cut-off frequency with the capacitor 29 and the resistor different in capacitance or resistance from the capacitor 19 and the resistor 16, and the cut-off frequency is calculated in the similar manner for the filter unit 2.
A problem is encountered in the prior-art filter circuit in operability due to the variable resistor 10 manually changed in resistance.